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3 years ago

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Mathematics

1 answer:

olchik [2.2K]3 years ago

3 0

Answer :

33, 56, 65

Explain :

a = 33

b = 56

c = 65

${c}^{2} = {33}^{2} + {56}^{2} \\ c = \sqrt{1089 + 3136} \\ c = 65$

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Could these triangles be congruent? yes, if ab ≅ de yes, if bc = 7 yes, if ab ≅ ef no, because the hypotenuses must have differe

Nitella [24]

Yes, the triangles are congruent if AB ≅ DE.

Criteria for the Congruency of two Triangles

If two triangles share the same sides and angles, they are said to be congruent triangles.

Triangles are tested for congruence using the following 4 criteria:

1) Angle-side-angle(ASA): Two angles and a side of a triangle are congruent if they are equal to two angles and the corresponding side of another triangle.

2) Side-side-side(SSS): Two triangles make congruent triangles if all three sides of one triangle are equal to three sides of another.

3) Side angle side(SAS): A triangle is congruent if its two sides and any included angles are equivalent to those of another triangle's two sides and corresponding angle.

4) Hypotenuse - leg(HL): If a triangle's hypotenuse and one of its legs are equal, then the triangle's hypotenuse and leg are also equal.

Checking for Congruency in the Given Triangles

ΔDEF and ABC have a equal angles, ∠F=∠B, as well as a pair of equal sides, DF = AC.

Thus, in order to satisfy the SAS criterion of congruent triangles, AB = DE

Learn more about Congruent Triangles here:

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Which of the following terms is mismatched with its example?

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What is the equation of the line that passes through the point (-1, -7) and has a slope of 2?

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Step-by-step explanation:

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3x - 6 = 2 - 5x how do i get x

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Answer:

x=0.875

Step-by-step explanation:

3x-6=2-5x

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3 years ago

SAT scores are normed so that, in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. as

vovangra [49]

Answer:

a) $P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

$P(Z>1.25)=1-P(Z$

b) $P(400$

$P(-1$

c) $z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(500,100)$

Where $\mu=500$ and $\sigma=100$

We are interested on this probability

$P(X>625)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.25)=1-P(Z$

Part b

We are interested on this probability

$P(400$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(400$

And we can find this probability with this difference:

$P(-1$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1$

Part c

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.8$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

8 0

3 years ago